document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94843>Question 94843</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if f(x)=(2-xsquare)<BR>\n" );
document.write( "how to solve :<BR>\n" );
document.write( "f(x+h)-f(x)    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69624 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=69624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2+-+x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=== call this equation 1<BR>\n" );
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document.write( "Next you need to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What this means is you return to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2+-+x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "you replace every x in that equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bh ALIGN=MIDDLE  ALT=\"x%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When you do that replacement you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+=+2+-+%28x%2Bh%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+=+2+-+%28x%2Bh%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=== call this equation 2<BR>\n" );
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document.write( "To simplify this you need to square the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bh ALIGN=MIDDLE  ALT=\"x%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the right side. Do this by multiplying:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bh%29%5E2+=+%28x%2Bh%29%2A%28x%2Bh%29+=+x%5E2+%2B2xh+%2B+h%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Bh%29%5E2+=+%28x%2Bh%29%2A%28x%2Bh%29+=+x%5E2+%2B2xh+%2B+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B2xh+%2B+h%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B2xh+%2B+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into equation 2 in place of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bh%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Bh%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and equation 2 becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+=+2+-+%28x%5E2+%2B+2xh+%2B+h%5E2%29+=+2+-+x%5E2+-+2xh+-+h%5E2 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+=+2+-+%28x%5E2+%2B+2xh+%2B+h%5E2%29+=+2+-+x%5E2+-+2xh+-+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=== call this equation 3<BR>\n" );
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document.write( "The problem asked you to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+-+f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+-+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From equation 3 we know that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+=+2+-+x%5E2+-+2xh+-+h%5E2 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+=+2+-+x%5E2+-+2xh+-+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and from equation 1 we know:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2+-+x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So we substitute the right side of these two equations into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+-+f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+-+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in place<BR>\n" );
document.write( "of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+-+f%28x%29+=+2+-+x%5E2+-+2xh+-+h%5E2+-+%282+-+x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+-+f%28x%29+=+2+-+x%5E2+-+2xh+-+h%5E2+-+%282+-+x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the right side, since the set of parentheses are preceded by a minus sign, the parentheses<BR>\n" );
document.write( "can be removed if we change the signs of the two terms in the parentheses. This makes the<BR>\n" );
document.write( "equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+-+f%28x%29+=+2+-+x%5E2+-+2xh+-+h%5E2+-+2+%2B+x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+-+f%28x%29+=+2+-+x%5E2+-+2xh+-+h%5E2+-+2+%2B+x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now on the right side you can notice that the +2 and the -2 cancel each other as does the <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2+ ALIGN=MIDDLE  ALT=\"-x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Those terms, therefore, disappear and you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29+-+f%28x%29+=+-+2xh+-+h%5E2 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29+-+f%28x%29+=+-+2xh+-+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem a little more.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );